I'm mostly interested in not only to 'hack' but to understand how computers and programs work and what things make them vulnerable at the first place.

The first thing is (I assume) to learn some programming language, and I'm currently reading C++ Primer (4th.ed.). But what should I read'n'learn after that? I know that programming is not so much about the language but to know how to solve problems. How can I train myself to 'think right' and learn to solve problems effectively?

And what would be good place to start getting familiar with the whole hacking theme? And most of all; what to do to really know what and why computer and programs are doing? There's really no point of 'hacking' if I don't really understand what I'm doing and why I'm doing it...

So, summa summarum: What book and other texts and things would you suggest to wannabe hacker?

You won't learn how to hack here, if it's your intention, you might as well part... You will however learn how things work with technology which could lead towards an understanding of the overall idea of "hacking".

Learning C++ is a great way to get started, I'd highly recommend learning C++ then Perl and PHP; I say Perl as it's highly used in *nix systems today, and PHP as it's one of the main internet technologies for serving content on webservers.

A good base to start learning is try to recreate what you download programs for... Such as, if you use IRC, try to build an IRC client; you'll then learn how the protocol works and how to communicate with the servers; from here you have a firm grip of the functionality and would be capable of looking for ways it could be improved upon and possibly find bugs in the process (which could lead towards discovering exploits)